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!                          234     ON  THE  COMPOSITION  AND  RESOLUTION  OF STREAMS OF
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embrace them all; and when such a theory has been arrived at, i                     and thoroughly verified, the task of deducing from it the results
|                     which ought to be observed under a combination of circumstances
:                     which has nothing to recommend it for consideration but its com-
;                     plexity, may well be abandoned for new and more fertile fields
of research. But in the present case certain difficulties seem ' ;                     to have arisen respecting the connexion between common and
elliptically polarized light which it needed only a more detailed
study of the laws of combination of polarized light to overcome;
and accordingly the subject may be deemed not wholly devoid of
importance.
The early part of the following paper is devoted to a demon-
H                             stration of various properties of elliptically polarized light, and
1 ,j'                         of oppositely polarized streams.    When two streams of light are
called oppositely polarized, it is meant that, so far as relates to ; '                    its state of polarization, one stream is what the other becomes
i                        when it is turned in azimuth through 90, and has its nature
reversed as regards right-handed and left-handed.    Most, if not .,    '                         all, of these properties have doubtless already occurred to per-
f;    i                        sons studying the subject, but I am not aware of any formal
demonstrations of them which have been published; and indeed some artifices were required in order to avoid being encumbered in the demonstrations with long analytical expressions. The combination of several independent polarized streams is next considered, and with respect to this subject a proposition is proved which may be regarded as the capital theorem of the paper. It is as follows.
When any number of independent polarized streams, of given !                         refrangibility, are mixed together, the nature of the mixture is
completely determined by the values of four constants, which are certain functions of the intensities of the streams, and of the azimuths and eccentricities of the ellipses by which they are respectively characterized; so that any two groups of polarized streams which furnish the same values for each of these four constants are optically equivalent.
It is a simple consequence of this theorem, that any group of polarized streams is equivalent to a stream of common light combined with a stream of elliptically polarized light from a different source. The intensities of these two streams, as well as